# SAT Math 2

#### Frank measured the amount of liquid that evaporated over a 12-day period from his container with l equaling ounces of liquid. At the end of the day too, it had lost 3 ounces. At the end of day seven, an additional 6 ounces. By the end of day 12, the container had lost one-third of what remained at the end of day seven. Which of the following represents the remaining amount of liquid in ounces in Frank's container at the end of day 12?

If l is the ounces of liquid and we're wanting to know how much was lost at the end of day 12, then we must start with what was lost at the end of day 7 (the 3 ounces from day 2+the 6 ounces from day 7 for a total of 9 ounces lost). So we have l-9, but we also know that at the end of day 12, the remaining amount is one-third of that total. So divide l-9 by 3, and Answer 3 is the only correct choice.

#### An entertainment superstore is running a special sale on DVDs and Blu-ray. DVDs (d) are priced at $8 during the sale while Blu-ray (b) are priced at $15. Each price point is a 20% reduction off the regular price. The sale pulls in $1,250 with 60 total units sold. During a regular day, DVDs and Blu-ray combine for around $800 in total sales while moving two-thirds the number of units on the special sale day. Solving which of the following systems of equations will reveal d and b sold during a regular day?

Since the problem is asking for the numbers of d and b on a regular sale day, Answer 1 is the only choice that rings true. d+b=40 (number of combined units) and 10d with $10 being the regular price of DVDs while $18.75 is the regular price of Blu-ray adding up to $800.

#### Blake earns base pay of $10 per hour at a clothing boutique. He also earns a certain percentage commission on sales. Blake worked an average of 37 hours per week over a two-week period. If he also helped broker $7,500 in sales and his total pay is $1,000 for the two-week period, approximately what percentage commission does he earn?

He earned $740 in base pay and $260 in commission on $7,500 of sales. Approximately 3.5% is $260. Answer 3 is correct.

#### If ^{(C+x)}_{x-3}=^{x+8}_{3}, which of the following could be an expression of C in terms of x?

STEP ONE. Cross-multiply. STEP TWO. Add -3x to both sides, thus isolating C. STEP THREE. Multiply both sides * 1/3 to simplify 3C to C. STEP FOUR. Break down the quadratic equation (x+6)(x-4). Answer 3.

#### Larry wants to complete a marathon in under 6 hours, but he knows he can't run the 26.2 miles the whole way. He'll need to run (r) and walk (w). If he is able to walk at four miles per hour and run at six miles per hour, which system of inequalities shows his total running and walking time?

Using the process of elimination, you can dismiss B, C, and D, right away because the run-walk values are reversed. Answer 1 is the correct choice.

#### In a crossbow manufacturing facility, a quality control expert tests a randomly selected group of 1000 crossbows. If the expert finds 17 of the randomly selected crossbows are defective, which of the following inferences would be most supported?

If 17 of the 1,000 are defective, that translates to around 1.7%. Read the statements carefully, and Answer 2 is the only one that is true.

#### If ^{-19}_{6}<-4z+7<^{-13}_{6}, what is the greatest possible integer value of 16z-28?

STEP ONE. Multiply -4 to change the middle expression to 16z-28. STEP TWO. Don't forget to reverse inequality signs. STEP THREE. Convert the two fractions bookending the inequality. STEP FOUR. Look at the options. You want the highest possible integer value to fit the expression. You know 16z-28 is higher than 10 and 11, but it can't be 13, so that leaves Answer 3.

#### Which of the following ordered pairs (j,k) is the solution to the system of equations below?

-12-4j=6k

4+^{7}_{4}k=^{-8}_{7}j

Simply plug in the pairs to both equations and get two true statements. Answer 4 is the correct choice.

#### In the expression ^{76}_{123y-5y}=1, what is the value of y?

STEP ONE. Cross-multiply to get rid of the unwieldy fraction.
STEP TWO. Set common denominators of 3y for the left side of the equation and subtract, leaving you with ^{-3}_{3y}, or ^{-1}_{y}.
STEP THREE. Cross-multiply again to isolate y.
STEP FOUR. Divide both sides of the equal sign by 7.
Answer 1 is the correct choice.

#### It's Presidential election season and a high school is holding a site-wide mock election. Here's how the students voted by grade.

10th Grade CLINTON .61 TRUMP .31 OTHER .08 TOTAL 1.00

11th Grade CLINTON .49 TRUMP .49 OTHER .02 TOTAL 1.00

12th Grade CLINTON .42 TRUMP .53 OTHER .05 TOTAL 1.00

Total CLINTON .50 TRUMP .44 OTHER .06 TOTAL 1.00

723 students voted for Hillary Clinton. Approximately how many students attend this school?

Divide the number of Clinton voters (723) by the percentage of vote that she won.

#### John is traveling to Ghana, where the Cedi is the monetary unit for purchasing goods and services. He decides to buy travelers checks, which he can then use as cash at any retail location. He pays $29.60 (a 7% fee) for the travelers checks on the total purchase, which equals 600 Cedi. If he is at a trading post and decides to trade a personal possession valued at $4500 USD, how many Cedi is the item worth at the same exchange rate?

Divide $29.60 by 7%. You'll get $422.857143. Divide this number by 600 Cedi for the exchange rate (.70476190). Divide $4,500 by this number for your final answer.

#### If three times a number is equal to that number minus 7, what is the number?

Let "a number" be x. Three times this is 3x. This is equal to x-7 (3x=x-7). Add a -x to isolate the number. This leaves you with 2x=-7. Divide by 2, and you're left with x=-3.5.

#### >The amount of skin samples that David needs for an experiment must be greater than 11 but less than or equal to 27. Which of the following represents an acceptable range for David's experiment?

Simply jot down the inequalities as they are presented in the word problem and match up to the answer selection. That leaves Answer 3.

#### If 2x+2y=0, which of the following must be equivalent to 2x-2y?

STEP ONE. Separate the two variables and get rid of the 0 (2x=-2y). STEP TWO. Divide by 2 (x=-y). STEP THREE. Plug in -y for x and solve. This leaves Answer 1.

#### Which of the following is equivalent to 4x^{2}-4x-48?

STEP ONE. Pull out your four to simplify the equation. STEP TWO. Solve for the two resulting equations. Answer 2 is the correct choice.

#### If 2a+3b=26 and 5a+4b=51, what is the value of a+b?

STEP ONE. Add the two equations (7a+7b=77). STEP TWO. Divide by 7 (a+b=11). Answer 4 is the correct choice.

#### If x^{2}+4xy+y^{2}=-44 and y-x=14, which of the following could be the value of x?

Simple enough answer choices. Simply plug in the numbers into the simpler equation. This will help produce a potential answer for y as well. You can then check your answers in both equations to make sure they "fit."

#### If three times a number (x) is equal to that number plus six, what is five times that number plus 20 minus that number?

A careful reading of the word problem will leave you with the following: 3x=x+6, 5x+20-x 3x=x+6 ADD -x 2x=6 DIVIDE by 2 x=3 5x+20-x=32 SIMPLIFY x 4x+20 SUBSTITUTE 3 for x, adds up to 32, Answer 3.

#### If 4y=y+4, what is the value of 3y?

Start with 4y=y+4. ADD -y to both sides 3y=4 DIVIDE by 3 y=4/3 SUBSTITUTE 4/3 for y and MULTIPLY * 3. SIMPLIFY FRACTION THROUGH DIVISION. Answer 4.

#### John joins a new specialty video streaming service for horror movie lovers. The cost is $5 per month (m) plus a one-time membership fee of $12. If John pays for his first two years in advance, which equation properly states his purchase?

The cost is $5 per month (5m). The +12 accounts for the one-time purchase price. To solve for the two-year question, you would simply need to plug 24 into m (for 24 months in two years). Since the question is not asking for the actual number, but the equation, Answer 1 is the correct choice.

#### >What is the value of (3x^{2}+5x+9)-(3x^{2}-5x+8)?

Simply remove the parentheses and solve. This leaves 10x+1, or Answer 2.

#### If a=^{6a2}/_{18} and a is a non-zero integer, which of the following is equivalent to a?

STEP ONE. Cross-multiply (18a=6a2). STEP TWO. Reverse (6a2=18a). STEP THREE. Divide by 6 (a2=3a). STEP FOUR. Take the square root of a (3√a). Answer 4.

#### A professional football team plays a 16 game season with a goal of averaging 44,000 per week in ticket sales. If the team averages 40,000 through the first five weeks of the year, how many will it need to average the rest of the year to come the closest to its target?

40,000*5 weeks of the year=200,000 Pick a number and start high since there is a lot of ground to make up to get to 44,000. 46,000*11 remaining weeks of the year=506,000 Add 506000+200000=706000. Divide this by 16. 44,125 is the answer, and since that's the closest you'll get to the target, Answer 1 is the correct choice.

#### In the equation 4x^{2}-20x=-24, what is one possible value of x?

Simply plug in your options, and you'll see that 3 is the only answer (Answer 3).

#### >What number (x) divided by four is equal to that same number minus 30?

x/4=x-30 CROSS-MULTIPLY. x=4(x-30) MULTIPLY. x=4x-120 ADD -4x -3x=-120 DIVIDE -3 x=40 Answer 2.

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